Question

Multiple Concept Example 9 deals with the concepts that are important in this problem. A grasshopper makes four jumps. The displacement vectors are (1) 26.0 cm, due west; (2) 20.0 cm, 60.0 ° south of west; (3) 24.0 cm, 58.0 ° south of east; and (4) 30.0 cm, 45.0 ° north of east. Find (a) the magnitude and (b) direction of the resultant displacement. Express the direction as a positive angle with respect to due west.

Answer 1

given

d1 = 26 cm

theta1 = 180 deg

d1x = 26cos180 = -26 cm

d1y = d1sin180 = 0

d2 = 20 cm

theta2 = 180+60 = 240 deg

d2x = 20cos240 = -10 cm

d2y = 20sin240 = -17.32 cm

d3 = 24 cm

theta3 = (360-58) = 302 deg

d3x = 24cos302 = 12.72 cm

d3y = 24sin302 = -20 35 cm

d4 = 30 cm

theta4 = 45 deg

d4x = 30cos45 = 21.2 cm

d4y = 30sin45 = 21.2 cm

resultant x acomponent Rx = d1x+d2x+d3x+d4x = -2.08 cm

resusltant y component Ry = d1y+d2y+d3y+d4y = -16.47 cm

a) magnitude = sqrt(RX^2+RY^2) = 16.6 cm

b) direction = theta = tan^-1(Ry/Rx) = 82.8 degrees from west